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The Poisson Matrix characteristic and the 3/2 blow up of the Hilbert transform
Komla Domelevo, Spyridon Kakaroumpas, Stefanie Petermichl +2
Recently the matrix conjecture was disproved. Indeed, the growth of the vector Hilbert transform in the matrix weighted space was shown to be at best a constant mult…
Extrapolation for bilinear compact operators in the variable exponent setting
Spyridon Kakaroumpas, Stefanos Lappas
We establish extrapolation of compactness for bilinear operators in the scale of weighted variable exponent Lebesgue spaces. First, we prove an abstract principle relying on the Co…
Matrix-weighted estimates beyond Calderón-Zygmund theory
Spyridon Kakaroumpas, Thu Hien Nguyen, Dimitris Vardakis
We investigate matrix-weighted bounds for the sublinear non-kernel operators considered by F. Bernicot, D. Frey, and S. Petermichl. We extend their result to sublinear operators ac…
Matrix-weighted little BMO spaces in two parameters
Spyridon Kakaroumpas, Odí Soler i Gibert
In this paper we set up a theory of two-matrix weighted little BMO in two parameters. We prove that being a member of this class is equivalent to belonging uniformly in each variab…
Boundedness of Journé operators with matrix weights
Komla Domelevo, Spyridon Kakaroumpas, Stefanie Petermichl +1
We develop a biparameter theory for matrix weights and provide various biparameter matrix-weighted bounds for Journé operators as well as other central operators under the assumpti…
Dyadic product BMO in the Bloom setting
Spyridon Kakaroumpas, Odí Soler i Gibert
Ó. Blasco and S. Pott showed that the supremum of operator norms over of all bicommutators (with the same symbol) of one-parameter Haar multipliers dominates the biparameter…
Two-weight estimates for sparse square functions and the separated bump conjecture
Spyridon Kakaroumpas
We show that two-weight bounds for sparse square functions, uniformly with respect to the sparseness constant of the underlying sparse family, and in both directions, do not…
"Small step" remodeling and counterexamples for weighted estimates with arbitrarily "smooth" weights
Spyridon Kakaroumpas, Sergei Treil
For an weight the norm of the Hilbert Transform in , is estimated by , where is the characteristic of the weight …
A note on a two-weight estimate for the dyadic square function
Spyridon Kakaroumpas
We show that the two-weight estimate for the dyadic square function proved by Lacey--Li in [2] is sharp.